A. f(x) = -x^2 - x - 4

B. f(x) = -x^2 + 4

C. f(x) = x^2 + 3x + 4

D. f(x) = x^2 + 4

Answer:

First Attachment : Option A,

Second Attachment : Option C

Step-by-step explanation:

We are given that,

z₁ = [tex]3(\cos ((\pi )/(6))+i\sin ((\pi )/(6)))[/tex] and z₂ = [tex]4(\cos ((\pi )/(3))+i\sin ((\pi )/(3)))[/tex]

Therefore if we want to determine z₁( z₂ ), we would have to find the trigonometric form of the following expression,

[tex]3(\cos ((\pi )/(6))+i\sin ((\pi )/(6)))*4(\cos ((\pi )/(3))+i\sin ((\pi )/(3)))[/tex]

( Combine expressions )

= [tex]12(\cos ( \pi /6+\pi / 3 ) + i\sin (\pi /6 +\pi / 3 )[/tex]

( Let's now add [tex]\pi / 6 + \pi / 3[/tex], further simplifying this expression )

[tex]\frac{\pi }{6}+\frac{\pi }{3} = \frac{\pi }{6}+\frac{\pi 2}{6} = \frac{\pi +\pi 2}{6} = \frac{3\pi }{6} = \pi / 2[/tex]

( Substitute )

[tex]12(\cos ( \pi /2 ) + i\sin ( \pi /2 ) )[/tex]

And therefore the correct solution would be option a, for the first attachment.

______________________________________________

For this second attachment, we would have to solve for the following expression,

[tex]\frac{3\left(\cos \left(\frac{\pi \:}{6}\right)+i\sin \left(\frac{\pi \:}{6}\right)\right)}{4\left(\cos \left(\frac{\pi \:}{3}\right)+i\sin \left(\frac{\pi \:}{3}\right)\right)}[/tex]

From which we know that cos(π/6) = √3 / 2, sin(π/6) = 1 / 2, cos(π/3) = 1 / 2, and sin(π/3) = √3 / 2. Therefore,

[tex]\:\frac{3\left(\cos \left(\frac{\pi }{6}\right)+i\sin \left(\frac{\pi }{6}\right)\right)}{4\left(\cos \left(\frac{\pi }{3}\right)+i\sin \left(\frac{\pi }{3}\right)\right)}:\quad \frac{3\sqrt{3}}{8}-i\frac{3}{8}[/tex]

[tex]\frac{3\sqrt{3}}{8}-i\frac{3}{8} = \frac{3\sqrt{3}}{8}-\frac{3}{8}i[/tex]

Our solution for the second attachment will be option c.

Answer:

Only one solution.

Step-by-step explanation:

y = 3x +2

y -2x =4

y - 2x = 4

=> y = 2x +4

y = 3x + 2

y = 2x + 4

Since both equations are not the same, so the answer cannot be "infinitely many solutions".

They both intersect each other 1 point, so it cannot be "no solutions".

So the answer is "Only 1 solution".

Answer:

a) Pr(drug user| positive test) = 0.3333

b) The probability that he will failed his first test = 0.9703

c) the probability that he is a drug user since  failed his second drug test

= 0.961165

Step-by-step explanation:

From the given information:

Suppose that 1% of the employees of a certain company use illegal drugs.

Probability of illegal drug user = 0.01

Probability of user that do not use drug = 1 - 0.01 = 0.99

From the person that is a illegal drug user, the company performs random drug tests that return positive results = 0.99

Therefore, the negative result for illegal drug user = 1 - 0.99 = 0.01

However, it also has a 2% false positive rate.

i.e the probability of the user that do not use drug has a positive result of 2% = 0.02

Thus, the probability of the user that do not use drug has a negative result of = 1 - 0.02

= 0.98

We are tasked to answer the following questions.

a) Steve, an employee at the company, has a positive test. What is the probability that he is a drug user?

i.e This employee we are taking about is a drug user and he has a positive test.

Thus;

Pr(drug user| positive test) = [tex]\dfrac{0.99 \times 0.01}{0.99 \times 0.01+ 0.02 \times 0.99}[/tex]

Pr(drug user| positive test) = [tex]\dfrac{0.0099}{0.0099+0.0198}[/tex]

Pr(drug user| positive test) = [tex]\dfrac{0.0099}{0.0297}[/tex]

Pr(drug user| positive test) = 0.3333

b) Knowing he failed his first test, what is the probability that Steve will fail his next drug test?

The probability that he will failed his first test = ((0.01 × 0.01) + (0.99×0.98))

The probability that he will failed his first test = ( 1 × 10⁻⁴ + 0.9702)

The probability that he will failed his first test = 0.9703

c)  Steve just failed his second drug test. Now, what is the probability that he is a drug user?

the probability that he is a drug user since he  failed his second drug test using Bayes theorem can be expressed as:

= [tex]\dfrac{0.01 \times(0.99\times 0.99)}{0.01 \times (0.99 \times0.99)+ 0.99(0.02 \times0.02)}[/tex]

the probability that he is a drug user since failed his second drug test

= [tex]\dfrac{0.01 \times(0.9801)}{0.01 \times (0.9801)+ 0.99(4 \times 10^{-4})}[/tex]

the probability that he is a drug user since  failed his second drug test

= [tex]\dfrac{0.009801}{0.009801+ 3.96 \times 10^{-4}}[/tex]

the probability that he is a drug user since  failed his second drug test

= 0.961165

Answer:

x + y = 200

0.08x + 0.24y = 0.18(200)

Step-by-step explanation:

x + y = 200

0.08x + 0.24y = 0.18(200)

The equations which describes the amount of 8% solution used and the amount of 24% solution used are: x+ y=200 and x+3y=450.

An equation is a relationship between two or more variables. They are mostly present in equal to form and are equated to find the value of variables present in them.

let the amount of 8% solution used be x and the amount of 24% solution used be y.

According to question the amount of total solution will be 200ml, So, the equation will be:

x +y=200

Now we have been said that the solution will be 18% saline and 8% saline mixture and 24% saline mixtures are used, So the next equation will be:

0.08x+ 0.24y=0.18*200

8x/100+24/100=18/100*200

8x+24y=3600

8(x+3y)=3600

x+3y=450

Hence the equations which shows the amount of solutions will be x+y=200 and x+3y=450.

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Answer:

800:1200 or  2:3

Step-by-step explanation:

400 payed

1200 in total

1200-400=800

800:1200 or 2:3

Answer:

[tex]\pi[/tex] radian

Step-by-step explanation:

We know that angle for a full circle is 2[tex]\pi[/tex]

In the given figure shape is semicircle

hence,

angle for semicircle will be half of angle of full circle

thus, angle for given figure = half of  angle for a full circle = 1/2 * 2[tex]\pi[/tex] = [tex]\pi[/tex]

Thus, answer is [tex]\pi[/tex] radian

alternatively, we also know that angle for a straight line is 180 degrees

and 180 degrees is same as [tex]\pi[/tex] radian.

Answer:

3.19 seconds

Step-by-step explanation:

Given:

Phone gets dropped from a Height = 150 ft

To find:

Time taken for the phone to reach the ground = ?

Solution:

First of all, let us learn about the formula of distance in terms of Initial speed u; Time t and Acceleration a:

[tex]s=ut+\dfrac{1}{2}at^2[/tex]

Here the phone is dropped from a height so a = g m/[tex]s^2[/tex] i.e. acceleration due to gravity.

g = 9.8 m/[tex]s^2[/tex]

s = 150 ft

Initial velocity, u = 0

Putting all the values in the formula:

[tex]150=0 t+\dfrac{1}{2}gt^2\\\Rightarrow 50=\dfrac{1}{2}\times 9.8 \times t^2\\\Rightarrow t^2=\dfrac{50}{4.9 }\\\Rightarrow t^2=10.20\\\Rightarrow t = 3.19\ sec[/tex]

So, the time taken is 3.19 seconds.

Answer:

x = 4

Step-by-step explanation:

2( 3x + 3) = 8x - 2

6x + 6 = 8x -2

6x + 8 = 8x

8 = 2x

4 = x

It is given that Y is the midpoint of XZ. If XZ = 8x − 2 and YZ = 3x + 3, So the value of x is x = 4.

Midpoint, as the word suggests, means the point which lies in the middle of something.

Midpoint of a line segment means a point which lies in the mid of the given line segment.

We have been given that Y is the midpoint of XZ. If XZ = 8x − 2 and YZ = 3x + 3, we need to find x.

We know that;

2(YZ) = XZ  

Substitute in the values

2( 3x + 3) = 8x - 2

Use the Distributive Property

6x + 6 = 8x -2

6x + 8 = 8x

8 = 2x

4 = x

Switch the sides to make it easier to read

x = 4

It is given that Y is the midpoint of XZ. If XZ = 8x − 2 and YZ = 3x + 3, So the value of x is x = 4.

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Answer: 250 mi

Step-by-step explanation:

Here we can think in a triangle rectangle:

The distance from Birmingham to Atlanta is roughly 150 mi, and this is one of the cathetus.

And the distance from Birmingham to Nashville is roughly 200 mi, this is the other cathetus of the triangle.

Now, the distance from Atlanta to Nashville will be the hypotenuse of this triangle rectangle.

Now we can apply the Pythagorean's theorem:

A^2 + B^2 = H^2

Where A and B are the cathetus, and H is the hypotenuse:

Then:

H = √(A^2 + B^2)

H = √(150^2 + 200^2) mi = √(62,500) mi = 250 mi

Then the estimated distance from Atlanta to Nashville is 250 mi

Answer:

the Sum

hope this helps

Answer:

277°

Step-by-step explanation:

The measure of arc AEG = AB + BE + EF + FG

The central angle is congruent to the arc that subtends it

∠ ECB = 180° - 44° = 136° ( adjacent angles )

∠ECF = ∠ ACB = 44° ( vertical angles ), thus

AEG = 44° + 136° + 44° + 53° = 277°

Answer:

Z > ± 1.645

z= 3.968

Step-by-step explanation:

We formulate the null and alternate hypotheses as

H0 =μ2 ≥ μ1   Ha: μ2  <μ1  one sided

Let α= 0.05

Since the sample sizes are large therefore the test statistic used under H0 is

The critical region for α= 0.05 for a one tailed test Z > ± 1.645

Z = (x`2- x`1) /s/ √n

Z= 154.8-128.746.5/√50

z= 26.1/6.577

z= 3.968

Since the calculated value of z lies in the critical region we reject H0 that internet users spend more time  or equal time.

Answer:

16

Step-by-step explanation:

[tex]\frac{8}{2} x (2+2) = \frac{8}{2} x 4 = \frac{8 x 4}{2} = \frac{32}{2} = 16[/tex]

Answer: 16

PEMDAS

P: Parenthesis

E: Exponents

M: Multipcaction

D: Divison

A: Addition

S: Subtraction

PEMDAS can be also known as Please Excuse My Dear Aunt Sally

P: (2+2)

E: N/A (There are no exponents)

M: 4×4

D: 8÷2

A: 2+2

S: N/A (There is nothing to subtract)

How did we get 4×4? We divided 8÷2 which got us 4. Then we added 2+2 and we also got 4. Then we multiplied 4×4 which got us 16. That's how 16 is our answer.

Answer:

Step-by-step explanation:

In order to find B we must first angle C

To find angle C we use the sine rule

That's

[tex] \frac{ |a| }{ \sin(A) } = \frac{ |c| }{ \sin(C) } [/tex]

From the question

a = 15

A = 70°

c = 14

So we have

[tex] \frac{15}{ \sin(70) } = \frac{14}{ \sin(C) } [/tex]

[tex] \sin(C) = \frac{14 \sin(7 0 ) }{15} [/tex]

[tex]C = \sin^{ - 1} ( \frac{14 \sin(70) }{15} ) [/tex]

C = 61.288

Since we've found C we can use it to find B.

Angles in a triangle add up to 180°

To find B add A and C and subtract it from 180°

That's

A + B + C = 180

B = 180 - A - C

B = 180 - 70 - 61.3

To find b we can use the sine rule

That's

[tex] \frac{ |a| }{ \sin(A) } = \frac{ |a| }{ \sin(B) } [/tex]

[tex] \frac{15}{ \sin(70) } = \frac{ |b| }{ \sin(48.7) } [/tex]

[tex] |b| = \frac{15 \sin(48.7) }{ \sin(70) } [/tex]

b = 11.9921

Hope this helps you

Answer:

√32

Step-by-step explanation:

Answer:

2009

Step-by-step explanation:

A deficit would be the least amount coming in (Revenues). and the most going out (Expenditures).  So you look for the biggest gap. It appears the gap is largest in 2009.

Answer:

False

Step-by-step explanation:

We also need to show that it is true for n=1

and for n=k+1

Answer:

Explained below.

Step-by-step explanation:

The ANOVA and Regression output for an application relating maintenance expense (dollars per month) to usage (hours per week) for a particular brand of computer terminal is provided.

(A)

The estimated regression equation equation is:

[tex]y=6.1092+0.8931x[/tex]

Here,

y = maintenance expense (dollars per month)

x = usage (hours per week) for a particular brand of computer terminal

(B)

Consider the Regression output.

The hypothesis to test whether monthly maintenance expense is related to usage is:

H₀: The monthly maintenance expense is not related to usage, i.e. β = 0.

Hₐ: The monthly maintenance expense is related to usage, i.e. β ≠ 0.

Compute the test statistic as follows:

[tex]t=\frac{b}{S.E._{b}}=\frac{0.8931}{0.149}=5.99[/tex]

Compute the p-value as follows:

[tex]p-value=2\times P (t_{8}<5.99}=0.00033[/tex]

The null hypothesis will be rejected if the p-value is less than the significance level.

p-value = 0.00033 < α = 0.05

Reject the null hypothesis.

(C)

Monthly maintenance expense​ is related to usage.

(D)

Yes, the estimated regression equation provide a good fit.

Since the regression coefficient is significant it can be concluded that the regression equation estimated is a good fit.

From the regression output given, the solution to the questions given are outlined thus ;

1.)

Regression equation :

Hence, the estimated regression equation is;

2.)

We can calculate the T-statistic value thus ;

Hence, the T-statistic is given as ;

[tex] T-statistic = \frac{0.8931}{0.149} = 5.99[/tex]

Pvalue (2 tailed) = 0.00033

Decison Region :

Since 0.00033 < 0.05 ; we reject the Null hypothesis.

3.)

Hence, we conclude that monthly expense is related to usage.

4.)

Since, the correlation Coefficient, β ≠ 0 ; Yes, the correlation provides a good fit as it is significant.

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Answer:

The area of larger triangle is 48 ft².

Step-by-step explanation:

Assuming that the area of triangle formula is A = 1/2 × base × height. Then, you have to substitute the following values :

[tex]area = \frac{1}{2} \times b \times h[/tex]

[tex]let \: b = 12,h = 8[/tex]

[tex]area = \frac{1}{2} \times 12 \times 8[/tex]

[tex]area = \frac{1}{2} \times 96[/tex]

[tex]area = 48 \: {feet}^{2} [/tex]

Given that;

A∞bh

A=kbh. where k is a constant

For smaller triangle

A=kbh

16=8(4)k

16=32k

k=½

For bigger triangle

A=kbh

Where k=½ , b= 12 and h=8

A=½(12)8

A=48 square feet

Answer:

Your question lacks some parts attached below is the complete question

Answer : 2.66

Step-by-step explanation:

The expected number ( E ) can be calculated using the formula below

[tex]E = \frac{row total * column total }{gross total}[/tex]

since we are computing the number of subjects that would prefer Linux operating system and are also rated as exceptional

The row total to be used = 53 ( row total of exceptional )

The column total to be used  = 13 ( column total of Linux )

The gross total to be used = summation of row total of both exceptional and no-exceptional = 259

BACK TO THE EQUATION

E = [tex]\frac{53*13}{259}[/tex]  = 689 / 259

E = 2.6602 ≈ 2.66

Answer:

  find the difference of points on the graph

Step-by-step explanation:

The cumulative frequency graph (CDF) represents the integral of the probability distribution function (PDF). You find the probability that X is in some interval by subtracting the value of the CDF at the low end of the interval from the CDF value at the high end of the interval.

  p(a < x < b) = cdf(b) -cdf(a)

Answer:

16 + 8b ≥ 50

4500

Step-by-step explanation:

He needs at least 50 rooms and has already reserved 16

They are in groups of 8

16 + 8b ≥ 50

Subtract 16 from each side

16+8b-16 ≥ 50 -16

8b≥ 34

Divide by 6

8b/8 ≥ 34/8

b≥ 4.25

We need to round up since we need at least 50

b = 5 since we want the least amount of rooms

Each block is 900

5*900 = 4500 more that he will have to spend

Answer:

23.6 (approximate value)

Step-by-step explanation:

Answer:

Step-by-step explanation:

23.6

Answer:  C) 50% of the students scored below 70%

Step-by-step explanation:

Mean is the average.  To find the mean (aka average) you add up all of the scores and divide by the number of tests.  

B) The mean can be 70 without any test scoring 70% so B is not true.

A) Since B is not true, then A is not a valid option.

D) We don't know any of the other data so don't know if it is skewed left, skewed right, or normal.  Therefore, option D is not true.

C) If the average is 70%, then half received grades above that score and half received grades below that score.  So, option C is TRUE!

Answer:

1 Cruz it makes sense I hope this helps tho

Answer:

46

Step-by-step explanation:

See attached for reference

The points given:

They form a rectangle as seen in the picture.

We can notice that this is a parallelogram, as respective lines have same difference of coordinates.

So calculating only the two of the sides will be sufficient to get its perimeter:

So, the perimeter:

Step-by-step explanation:

( secA + 1)( sec A - 1)

Using the expansion

( a + b)( a - b) = a² - b²

Expand the expression

We have

sec²A + secA - secA - 1

That's

sec² A - 1

From trigonometric identities

So we have the final answer as

As proven

Hope this helps you

Step-by-step explanation:

Here,

LHS

= (SecA+1)(secA -1)

[tex] = {sec}^{2} A - 1[/tex]

[tex]{as{a}^{2} - {b}^{2} =(a + b)(a - b)[/tex]

Now, we have formula that:

[tex] {sec}^{2} \alpha - {tan \alpha }^{2} = 1[/tex]

[tex] {tan}^{2} \alpha = {sec }^{2} \alpha - 1[/tex]

as we got ,

[tex] = {sec}^{2} A- 1[/tex]

This is equal to:

[tex] = {tan}^{2} A[/tex]

= RHS proved.

Hope it helps....

Answer:

12/155

Step-by-step explanation:

Total number of cookies:

Probability of getting a peanut butter cookie at first attempt is 9 out of 31:

Probability of getting a peanut butter cookie at second attempt is 8 out of 30 as one already taken and the total number has changed as well:

Probability of getting 2 peanut butter cookies is the product of each probability we got above:

Answer:

It has been proved that T is compact

Step-by-step explanation:

To prove this using the definition of compactness, let's assume that T is

not compact. Now, if that be the case, an open cover of T will exist. Let's call this open cover "A". Now, this open cover will have no finite subcover.

Now, from the question, since T is closed, it’s complement R\T will be open.

Therefore, if we add the set R\T to the collection of sets A, then we'll have an open cover of R and also of S.

Due to the fact that S is compact, this

cover will have a finite sub - cover which we will call B.

Finally, either B itself or B\{R\T} would be a finite sub - cover of A. This is a contradiction.

Thus, it proves that T has to be compact if S is to be a compact subset of R and T is to be a closed subset of S.

Answer:

-50

Step-by-step explanation:

Basically get two slopes -50(1)+100 will get you 1,50 (1 is x and 50 is y since its the answer)

-50(0)+100 (0,100)  Y₂-Y₁/X₂-X₁ 50-100/1-0

Rate of change per month = -$50